Most puzzles are not very interesting. :) But some are surprisingly rich, and those are the good ones to put in front of candidates in my opinion. E.g., I work

Most puzzles are not very interesting. :) But some are surprisingly rich, and those are the good ones to put in front of candidates in my opinion. E.g., I worked on one puzzle before I left ITA that involved laying out train track pieces to create a complete circuit within a rectangular region. (I don't believe this one has ever been used, but I could be wrong about that.) It was pretty interesting to solve this heuristically, but it turned out to involve something much deeper: the theory of so-called "lattice animals" -- an active area of research I knew nothing about. Lattice animals include polyominoes, which are probably familiar to most HN readers, but subsume other graph-related objects as well. I didn't know much about these, and ended up reading a bunch of cool papers on them as part of working on the puzzle. So at least for me, good puzzles have catalyzed some learning.